A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 567567 cubic feet. The concrete for the base costs $22 per square foot, the material for the roof costs $55 per square foot, and the material for the sides costs $4.504.50 per square foot. Find the dimensions of the most economical shed.

length of the base = 9 ft

and height of the shed = 7 ft

Step-by-step explanation:

given data

volume =  567 cubic feet

base costs = $2 per square foot

roof costs = $5 per square foot

sides costs $4.50 per square foot

solution

we take here length of the base = x ft

and height of the shed = y ft

so Volume will be express as

volume = x²× y

567 =  x² × y

y =  

and

we know  cost of material is express as here

cost of material  = cost of base + cost top + cost 4 side   ..................1

put here value

cost  = x²(2) + x²(5)  + 4xy (4.5)

cost = 7x² + 18xy

put here y  value

cost =   7x² + 18 x ( )

differentiate and  we get

C' = 14x -  

we put here C' = 0 and we get

14x -   = 0

solve it we get

x = 9 ft

and

y =  

y = 7 ft

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!